Two trains, Train A, and Train B, simultaneously depart Station A and Station B. Station A, and Station B are 252.5 miles apart from each other. Train A is moving at 124.7mph towards Station B, and Train B is moving at 253.5mph towards Station A. If both trains departed at 10:00 AM and it is now 10:08, how much longer until both trains pass each other?
To determine the time it takes for both trains to pass each other, we need to calculate their relative speed, and then divide the distance between them by this speed.
1. Calculate the relative speed:
- Train A is moving towards Station B at 124.7 mph.
- Train B is moving towards Station A at 253.5 mph.
- The relative speed of the two trains is the sum of their individual speeds: 124.7 mph + 253.5 mph = 378.2 mph.
2. Calculate the time it takes for the trains to pass each other:
- The distance between Station A and Station B is given as 252.5 miles.
- Since both trains departed at 10:00 AM, they have been traveling for 8 minutes (10:08 AM - 10:00 AM).
- Convert 8 minutes to hours by dividing by 60 (1 hour = 60 minutes): 8 minutes ÷ 60 = 0.133 hours.
- Add the travel time to the current time of 10:08 AM: 10:00 AM + 0.133 hours = 10:08 AM + 0.133 hours = 10:08 AM + 8 minutes = 10:16 AM.
3. Calculate the remaining distance for the trains to pass each other:
- Since they have been traveling for 8 minutes, Train A has covered 124.7 mph × 0.133 hours = 16.5891 miles.
- The remaining distance for the trains to pass each other is 252.5 miles - 16.5891 miles = 235.9109 miles.
4. Calculate the time it takes for the trains to cover the remaining distance:
- Divide the remaining distance by the relative speed: 235.9109 miles ÷ 378.2 mph ≈ 0.623 hours.
- Convert 0.623 hours to minutes by multiplying by 60: 0.623 hours × 60 = 37.38 minutes.
Therefore, it will take approximately 37.38 minutes for both trains to pass each other from the current time of 10:08 AM.
combined speed = 378.2 mi/hr
distance covered in 8 minutes: 378.2 * 8/60 = 50.4 mi
remaining distance: 202.1 mi
remaining time: 202.1/378.2 = 0.534 hours
Let the time taken for them to meet be t hrs
124.7t + 253.5t = 252.5
...
t = .6676.. hrs
= 40.058 minutes
since the trains have already travelled 8 minutes, it will take
about 32 more minutes.